Синтез регулятора для нелинейных объектов с запаздыванием методом разделения движений с применением критериев устойчивости

Abstract

Controllers and feedback are applied for performing many technical tasks, for example, maintaining the desired temperature stabilization in the thermostat and speed electric motor stabilization. Different methods such as the time-scale separation method, the frequency-response design method, and the Ziegler–Nichols method are applied to design controllers. The Ziegler–Nichols method does not provide the required transient process quality. The Smith predictor is sometimes applied to control objects with a transport delay. However, it may be difficult to apply the Smith predictor when a mathematical model is not fully known. There is a paper where the application of the motion separation method with a delay is considered. However, the calculation method proposed in that work requires solving a system of four nonlinear equations for a second-order object. Therefore, in this paper, we investigate the possibility of a simpler method for calculating the controller, namely, the possibility of using the Mikhailov criterion in the synthesis of a controller by the motion separation method for nonlinear objects with a delay. Also, the application of the Nyquist stability criterion with a simpler than the proposed earlier calculation procedure is considered in the paper. The values of the regulator coefficients obtained using the Nyquist criterion and the Mikhailov criterion are compared. The Mikhailov criterion and the Nyquist criterion are applied to estimate the stability of the fast motions subsystem. The derivation of formulas to calculate the parameters of the controller designed by the motion separation method for first-order non-linear objects with transport delays and second-order non-linear objects with transport delays with the use of the Mikhailov criterion is also considered in the paper. Transient processes are studied by numerical simulation. Transient processes plots are also given. The parameters of the controller that are needed to improve the performance of transient processes in the presence of a delay are found. The Peltier element, an aircraft strength test stand, a thermostat, and equipment for metal rolling are non-linear control objects with a transport delay. The Mikhailov hodographs for objects with a transport delay are presented.